Frana Allen - SKinner School  

The Ups and Downs of Graphing 

Frana Allen                    Skinner School  
                               111 South Throop
                               CHICAGO IL 60607
                               (773) 534-7790 

Objective(s):

The students (grades 4 through 8) will be able to: distinguish between  
qualitative and quantitative experiments, define manipulated, responding and 
controlled variables, graphing, horizontal and manipulating axis, 
extrapolation and interpolation. 

Materials Needed: 

Individual Activity:  graph paper, colored pencils, pencil and paper, a 
transparent ruler 

Strategy: 
    
    For the teacher:  (Teacher's language is important don't let it hang YOU 
up....Have fun with this, MY KIDS DID!)  Teachers.....This is an introduction to 
the quantitative approach to science that I feel is easy to learn.  I remind the 
students through visual aides the difference between quantitative and 
qualitative approach to science graphing.  Note: It is imperative that the 
students are ready to graduate from bar graphs to point graphs.  I explain to 
the students that the point graph replaces the bar with a dot or point at the 
center of the top of the bar.  Using the chalkboard, I have the students write 
the definitions of the terms they will use in doing the experiment.  Graphing is 
fun.....but, there are certain facts one must keep in mind when doing 
graphing...I remind the students that all the data points are not going to fit 
perfectly; however, we must really try to fit them perfectly.  We must fit a 
straight line through the area of the data points.  It should be noted that if 
they do obtain data points that do not fit a straight line, it is due to the 
problems in obtaining the data, unsteady hand, and or a poor read.  To assure a 
good fit, also, known as the best fit line, remind the students that they should 
make as many points on the graph as possible.(At least 3).  When students look 
at the data points on a graph to draw a conclusion it is called, interpolation. 
Sometimes experiments require students to make a prediction beyond the last data 
the last data point this is called extrapolation.                       

It is important that the students know that in this experiment they will be 
counting in centimeters (cm). 

Part 2
                            BOUNCING BALL EXPERIMENT

Materials:
Cooperative Groups of 3---2 meter sticks, 1 tennis ball, 1 super ball, strip 
of masking tape, 1 additional sheet of graph paper.   Note: This is one group 
set up. 


Procedure:
1.  Remember each students should have a job
        Recorder, materials gatherer, director, experimentor, etc.
2.  Go over the vocabulary used in the experiment
3.  Go over the expectations you want each student and group of students to do
4.  Read the procedure with the students
5.  If you find it necessary, demonstrate the set up

Performance Assessment: 

Bouncing Balls Data Sheet
Label drawing of experiment.  Note: H1 is the release height and H2 the bounce 
height.  Label H1 and H2 in your drawing. 
1.  Which is manipulated variable?
2.  Which is the responding variable?
3.  What variables are held fixed during the experiment?
4.  Why is it a good idea to carry out at least three trails for each value of 
    H1? 
5.  Why did you take an average numerical value H2?

......Graphing.................... 
 
Note:  You are going to plot the averages of the tennis ball and the super ball 
on the same graph.  Use colored pencils to identify the ball i.e. green for 
tennis ball and blue for tennis ball. 
Work together and use your notes...................

Answer the following questions:
1. On which axis (horizontal or vertical) did you plot the manipulated variable? 
2. On which axis (horizontal or vertical) did you plot the responding variable?
3. Did you plot your data according to the sequence (H2, H1) or (H1,H2)?
4. Is (O,O) a data point?_________________Why?_________________________

Conclusions: 

The students will be able to answer the following questions with 80% accuracy.

Bouncing Ball Experiment
1.  What type of experiment was this?
2.  Is the type of ball qualitative or quantitative?
3.  What are the two main variables on this experiment?

Using the graph you just did.........answer the questions 1-4
1.  If the release height of the tennis ball is 60 cm, what is the rebound 
    height?
    Did you use interpolation or extrapolation?
2.  If the release height of the tennis ball is 160 cm, what is the rebound 
    height?
    Did you use interpolation or extrapolation?
    Check your prediction experimentally.  Was your answer approximately 
    correct?
3.  If the tennis ball rebounds to a height of 140 cm, from what height was it 
    released?
    Did you use interpolation or extrapolation?
4.  If the release height of the super ball is one meter, what is the rebound 
    height?
    Did you use interpolation or extrapolation?   

References:

AIMS Program on Geometry and Graphing
CPS Qualitative Approach to Science '93